# Bounce Diagrams

Bounce Diagrams.
The bounce diagram can be a useful tool for the analysis of unitstep and pulse voltage responses of TLs. In the bounce diagram, distance is shown along the horizontal axis and time along the vertical axis. A series of lines is drawn diagonally on this diagram indicating the leading or trailing edges of a voltage (or current) waveform, which are labeled by the amplitude of the voltage (or current) for that time and position on the TL. It is helpful to present the bounce diagram with an example. Consider the TL shown below with a unit-step excitation.
The sloping lines indicate voltage waves traveling in the +z and -z directions. Each sloping line in this case is labeled with the voltage amplitude of the partial voltage wave traveling in that direction. We could also construct a bounce diagram for the amplitudes of a current wave.  These voltage amplitudes are obtained by multiplying the “incident” voltage by the reflection coefficient at the particular discontinuity (either tL or ts ) as shown.
The bounce diagram can be used in two ways: To determine the voltage variation
1. along the TL at a specific time,
2. at a specific z as a function of time.
These two cases will be considered separately below.
Use Bounce Diagram for V(z,t) vs. z at a Fixed t
For this illustration, we’ll assume a fixed time t0 is as shown in the bounce diagram above between 2tL and 3tL . To use the bounce diagram in this capacity:
(i.) Mark t0 on the vertical t axis.
(ii.) Draw a horizontal line at t0 .
(iii.) Draw a vertical line at the intersection. Only times before t0 are relevant, which is the portion of the graph “above” t0 .
(iv.) The voltage on the TL to the left of z0 is the sum of all voltages intersecting an imaginary vertical line at z0- as (v.) The voltage on the TL to the right of z0 is the sum of all voltages intersecting an imaginary vertical line at z0++ as: Example N14.1: Repeat Example N13.1 using a bounce diagram. Sketch the voltage on the TL at the time t0 = 4.5 ms.
For this TL, We can use the bounce diagram on page 2 for this example because the t0 in the bounce diagram is located at 4.5 ms as needed here for this example.
Consequently, from (1): while from (2): Sketch: This is the same voltage as shown in
Use Bounce Diagram for V(z,t) vs. t at a Fixed z  To use the bounce diagram in this situation:
(i.) Pick a position z0 at which to plot V (( z0,t )) versus time.
(ii.) Draw a vertical line at z0. It intersects the sloping lines at points P1 through P6 above.
(iii.) At each of these intersection points, draw horizontal lines and label these times t1 through t6. These are the times at which new wave fronts arrive and abruptly change the voltage at z0.
(iv.) The voltage at z0 versus time is then: Example N14.2: Consider the coaxial cable shown below. Sketch the voltage at the load V( (L,t) ) for the indicated unit-step input voltage and an open circuit load. For this TL circuit:  At time t = 0+, draw the equivalent lumped-element circuit at the input to the TL: By voltage division in this circuit Draw a vertical line at z0 = L in the bounce diagram. Then: 